Secure two-dimensional tori are flat

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dc.creatorBangert, Victor
dc.creatorGutkin, Eugene
dc.date2008-06-22
dc.date.accessioned2026-07-07T09:46:06Z
dc.date.available2026-07-07T09:46:06Z
dc.descriptionA riemannian manifold is secure if the geodesics between any pair of points in the manifold can be blocked by a finite number of point obstacles. Compact, flat manifolds are secure. A standing conjecture says that these are the only secure, compact riemannian manifolds. The conjecture claims, in particular, that a riemannian torus of any dimension is secure if and only if it is flat. We prove this for two-dimensional tori.
dc.description15 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0806.3572
dc.identifierhttp://arxiv.org/abs/0806.3572
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163413
dc.subjectDynamical Systems
dc.subjectDifferential Geometry
dc.subject37D40, 37E99, 53C22
dc.titleSecure two-dimensional tori are flat
dc.typetext

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